F2L or First Two Layers is the second step of the CFOP method, which aims to solve the first two bottom layers of a 3x3. Each algorithm solves a pair (an edge and a corner) into their designated location.
Each case is recognized by the position and orientation of the two pieces in relation to the target slot. Since there are four possible target slots, each case has four variants to avoid rotations.
The basic 41 cases deal with all permutations where the two pair pieces are on the U layer and/or in the target slot.